What are the chances that the plug could be powered with an internal lithium ion battery ans still look pretty good. While the whole point of the system is to be plugged in, I think that such a small board lends itself to a portable application. The 5 volt Dc could easily be supplied by an external battery back, but that is not so compact.

An internal battery would work but would require a charger system as well.

My guess is it wont work below 4.5v reliably. I have not studied its circuits, but it probably generates first a 5v and then all other volatages are regenerated with dc-dc tiny supplies inside. Because of those secondary supplies, it may even work done to 4.4 at the 5v input; otherwise most would start becoming unreliable at 4.7v. So your best bet is 4x NiMh inside, if you allow for a fatter plug; with a modern set of 2600mah AAAs, that could run for 3 to 4 hours without any external devices during the first year of the battery life; or you have to use 2x LiIo. I would be interested in your experimental results.

You also need to look at the other USB devices being loaded into the unit. Using NIMH is more economical and will give longer life than other cell types but you need to take care if you are planning on recharge plus power. Nimh battery protection is harder to source than Lithium Poly cells etc.